- #1

Karlisbad

- 131

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For the function ## y=f(x) ## is there a test to prove if its roots are real or either has some complex roots?, or in more general cases:

## y=g(x)D^{k}f(x) ## k>0 and a real D=d/dx number.

The question is that sometimes it can be very deceiving to tell if a function has real or complex roots, for example:

## y=exp(2 \pi x)-1 ## has only real roots.. but for real x the function ## y=exp(x^2)+1 ## has only complex roots , but for every real x the function is real.

## y=g(x)D^{k}f(x) ## k>0 and a real D=d/dx number.

The question is that sometimes it can be very deceiving to tell if a function has real or complex roots, for example:

## y=exp(2 \pi x)-1 ## has only real roots.. but for real x the function ## y=exp(x^2)+1 ## has only complex roots , but for every real x the function is real.

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